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<h1 class="reftitle">getFacet</h1>
<h2>Purpose</h2>
<p>Extract facet of the polyhedron specified by the inequality index.</p>
<h2>Syntax</h2>
<pre class="synopsis">Q = P.getFacet()</pre>
<pre class="synopsis">Q = P.getFacet(index)</pre>
<h2>Description</h2>
<p></p>
        Extract the facet of the polyhedron <img src="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/getfacet1.png" alt="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/getfacet1.png"> specified by the inequality <tt>index</tt>. The returned
        polyhedron <img src="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/getfacet2.png" alt="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/getfacet2.png"> is formed by rewriting this ineqality as equality constraint.                
        The polyhedron <img src="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/getfacet3.png" alt="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/getfacet3.png"> is given as
        <p class="programlistingindent"><img src="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/getfacet11.png" alt="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/getfacet11.png"></p>
        Given the <tt>index</tt>, the polyhedron <img src="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/getfacet4.png" alt="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/getfacet4.png"> is built as
        <p class="programlistingindent"><img src="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/getfacet12.png" alt="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/getfacet12.png"></p>
        The polyhedron <img src="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/getfacet5.png" alt="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/getfacet5.png">  must be given in its minimal representation (irredundant) H-representation, 
        otherwise an error is thrown. 
        
	<h2>Input Arguments</h2>
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<td><tt>P</tt></td>
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<p></p>Polyhedron in H-representation<p>
	    		Class: <tt>Polyhedron</tt></p>
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<td><tt>index</tt></td>
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<p></p>Index of a facet from polyhedron <img src="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/getfacet6.png" alt="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/getfacet6.png"> which is less or equal than the number of hyperplanes defining <img src="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/getfacet7.png" alt="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/getfacet7.png">.
	  If omited, all facets will be returned as a polyhedron array.<p>
	    		Class: <tt>double</tt></p>
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<h2>Output Arguments</h2>
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<td><tt>Q</tt></td>
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<p></p>Polyhedron <img src="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/getfacet8.png" alt="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/getfacet8.png"> that represents lower-dimensional facet of the Polyhedron <img src="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/getfacet9.png" alt="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/getfacet9.png">.<p>
	    		Class: <tt>Polyhedron</tt></p>
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<h2>Example(s)</h2>
<h3>Example 
				1</h3>Create random polyhedron <img src="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/getfacet10.png" alt="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/getfacet10.png"> and make it irredundant.<pre class="programlisting"> P = ExamplePoly.randHrep; </pre>
<pre class="programlisting"></pre>
<pre class="programlisting"> P.minHRep(); </pre>
<pre class="programlisting"></pre> Extract the third facet of the polyhedron. <pre class="programlisting"> Q = P.getFacet(3); </pre>
<pre class="programlisting"></pre> Plot the polyhedra.<pre class="programlisting"> P.plot; hold on; Q.plot('LineWidth',3,'LineStyle','-.'); </pre>
<pre class="programlisting"></pre>
<p class="programlistingindent"><img src="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/getfacet_img_1.png" alt="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/getfacet_img_1.png" width="60%"></p>
<h2>See Also</h2>
<a href="./isadjacent.html">isadjacent</a><p></p>
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<br><p>©  <b>2010-2013</b>     Martin Herceg: ETH Zurich,    <a href="mailto:herceg@control.ee.ethz.ch">herceg@control.ee.ethz.ch</a></p>
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